73 research outputs found
The Mirrors Model : Macroscopic Diffusion Without Noise or Chaos
We first clarify through classical examples the status of the laws of
macroscopic physics as laws of large numbers. We next consider the mirrors
model in a finite -dimensional domain and connected to particles reservoirs
at fixed chemical potentials. The dynamics is purely deterministic and
non-ergodic. We study the macroscopic current of particles in the stationary
regime. We show first that when the size of the system goes to infinity, the
behaviour of the stationary current of particles is governed by the proportion
of orbits crossing the system. This allows to formulate a necessary and
sufficient condition on the distribution of the set of orbits that ensures the
validity of Fick's law. Using this approach, we show that Fick's law relating
the stationary macroscopic current of particles to the concentration difference
holds in three dimensions and above. The negative correlations between crossing
orbits play a key role in the argument
Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation
We report an experimental evidence of a global bifurcation on a highly
turbulent von Karman flow. The mean flow presents multiple solutions: the
canonical symmetric solution becomes marginally unstable towards a flow which
breaks the basic symmetry of the driving apparatus even at very large Reynolds
number. The global bifurcation between these states is highly subcritical and
the system thus keeps a memory of its history. The transition recalls
low-dimension dynamical systems transitions and exhibits a very peculiar
statistics. We discuss the role of turbulence in two ways: the multiplicity of
hydrodynamical solutions and the effect of fluctuations on the nature of
transitions.Comment: submitted to Physical Review Letters 19 May 2004, accepted 10
September 200
Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment
The intention of the ''von Karman sodium'' (VKS) experiment is to study the
hydromagnetic dynamo effect in a highly turbulent and unconstrained flow. Much
effort has been devoted to the optimization of the mean flow and the lateral
boundary conditions in order to minimize the critical magnetic Reynolds number
and hence the necessary motor power. The main focus of this paper lies on the
role of ''lid layers'', i.e. layers of liquid sodium between the impellers and
the end walls of the cylinder. First, we study an analytical test flow to show
that lid layers can have an ambivalent effect on the efficiency of the dynamo.
The critical magnetic Reynolds number shows a flat minimum for a small lid
layer thickness, but increases for thicker layers. For the actual VKS geometry
it is shown that static lid layers yield a moderate increase of the critical
magnetic Reynolds number by approximately 12 per cent. A more dramatic increase
by 100 until 150 per cent can occur when some rotational flow is taken into
account in those layers. Possible solutions of this problem are discussed for
the real dynamo facility.Comment: 24 pages, 11 figures, minor changes, to appear in European Journal of
Mechanics B/Fluid
Supercritical Eckhaus Instability for Surface-Tension-Driven Hydrothermal Waves
International audienceWe study the nonlinear dynamics of hydrothermal waves produced by a surface-tension-driven convective flow in a long and thin annular channel heated from the side. Above onset, the supercritical traveling wave pattern undergoes a secondary instability: a supercritical Eckhaus instability. This leads to a small-wave-number phase-modulated nonlinear mode, and shows the first experimental evidence of a nonlinearly saturated phase instability mode for traveling wave patterns. At higher forcing level, this secondary pattern is subject to a tertiary instability. This mode is an amplitude mode characterized by traveling hole patterns, i.e., space-time defects that change the wave numbe
Supercritical transition to turbulence in an inertially-driven von Karman closed flow
We study the transition from laminar flow to fully developed turbulence for
an inertially-driven von Karman flow between two counter-rotating large
impellers fitted with curved blades over a wide range of Reynolds number (100 -
1 000 000). The transition is driven by the destabilisation of the azimuthal
shear-layer, i.e., Kelvin-Helmholtz instability which exhibits
travelling/drifting waves, modulated travelling waves and chaos below the
emergence of a turbulent spectrum. A local quantity -the energy of the velocity
fluctuations at a given point- and a global quantity -the applied torque- are
used to monitor the dynamics. The local quantity defines a critical Reynolds
number Rec for the onset of time-dependence in the flow, and an upper
threshold/crossover Ret for the saturation of the energy cascade. The
dimensionless drag coefficient, i.e., the turbulent dissipation, reaches a
plateau above this finite Ret, as expected for a "Kolmogorov"-like turbulence
for Re -> infinity. Our observations suggest that the transition to turbulence
in this closed flow is globally supercritical: the energy of the velocity
fluctuations can be considered as an order parameter characterizing the
dynamics from the first laminar time-dependence up to the fully developed
turbulence. Spectral analysis in temporal domain moreover reveals that almost
all of the fluctuations energy is stored in time-scales one or two orders of
magnitude slower than the time-scale based on impeller frequency
Ondes hydrothermales non-linéaires dans un disque et un anneau
URL: http://www-spht.cea.fr/articles/S98/109Nous nous intéressons à la convection thermocapillaire, produite par l'imposition d'un gradient {\it horizontal} de température sur une mince couche de fluide avec surface libre. En géométrie bidimensionnelle nous observons deux modes différents en compétition, tandis qu'en géométrie bidimensionnelle avec conditions limites périodiques, nous étudions la transition à la turbulence d'une onde propagative homogène
Fluctuation-Dissipation Relations and statistical temperatures in a turbulent von K\'arm\'an flow
We experimentally characterize the fluctuations of the non-homogeneous
non-isotropic turbulence in an axisymmetric von K\'arm\'an flow. We show that
these fluctuations satisfy relations analogous to classical
Fluctuation-Dissipation Relations (FDRs) in statistical mechanics. We use these
relations to measure statistical temperatures of turbulence. The values of
these temperatures are found to be dependent on the considered observable as
already evidenced in other far from equilibrium systems.Comment: four pages 2 figures one tabl
Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II: Convective/absolute transitions
We present experimental results on hydrothermal waves in long and narrow 1D
channels. In a bounded channel, we describe the primary and secondary
instabilities leading to waves and modulated waves in terms of
convective/absolute transitions. Because of on the combined effect of finite
group velocity and of the presence of boundaries, the wave-patterns are
non-uniform in space. We also investigate non-uniform wave-patterns observed in
an annular channel in the presence of sources and sinks of hydrothermal waves.
We connect our observations with the complex Ginzburg-Landau model equation in
the very same way as in the first part of the paper (nlin.PS/0208029).Comment: 37 pages, 23 figures (elsart.cls + AMS extensions). Accepted in
Physica D. See also companion paper "Nonlinear dynamics of waves and
modulated waves in 1D thermocapillary flows. I: General presentation and
periodic solutions" (nlin.PS/0208029). A version with high resolution figures
is available on N.G. webpag
On the properties of steady states in turbulent axisymmetric flows
We experimentally study the properties of mean and most probable velocity
fields in a turbulent von K\'arm\'an flow. These fields are found to be
described by two families of functions, as predicted by a recent statistical
mechanics study of 3D axisymmetric flows. We show that these functions depend
on the viscosity and on the forcing. Furthermore, when the Reynolds number is
increased, we exhibit a tendency for Beltramization of the flow, i.e. a
velocity-vorticity alignment. This result provides a first experimental
evidence of nonlinearity depletion in non-homogeneous non-isotropic turbulent
flow.Comment: latex prl-stationary-051215arxiv.tex, 9 files, 6 figures, 4 pages
(http://www-drecam.cea.fr/spec/articles/S06/008/
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